THE ELECTRON CONFIGURATION OF GROUND STATE OF THE ELEMENTS
THE
BENJAMIN CARROLL The Newark Colleges, Rutgers University, Newark, New Jersey ALEXANDER LEHRMAN The City College, New York City
THERE IS an increasing tendency in the teaching of college chemistry to describe the behavior of elements in terms of the electron configuration of their atoms. Use is made of both the principal quantum number, n, and the orbital angular momentum quantum number, 1. Valence (I), bond angles, bond strengths ( f ) ,magnetic properties, as well as acidic and basic behavior (5) are some of the phenomena of which even a somewhat elementary treatment requires a knowledge of the electron configurations. The electron configuration of the atoms can be obtained from a list such as is given in the table or chart, but unless one uses such table or chart it is necessary to know a t which atomic number each shell or subshell begins to be occupied by electrons. The configuration of an atom of an intervening element can then be found in most cases by interpolation. The existence of simple rules that could be used to formulate the electron configuration would aid in inducing teachers to discard the oversimplified and overworked octet theory of valence in favor of the modern treatment of valency which makes use of the n and 1 quantum numbers. It is the purpose of this article to suggest a rule which can greatly simplify the problem of writing the electron configuration of the ground state of an atom of any number from 1 to 96 in terms of the n and 1 quwtum numbers. By the ground state is meant that state of the atom in which the electrons are in the lowest possible energy levels. I t will be remembered that the principal quantum number, n, has integer values, 1 , 2 , . . .and that the quantum mechanical requirement for 1 is such that it can take only values of 0, 1,2, . . . (n- 1). The symbol for the n and 1 quantum numbers of an electron is the numerical value of n followed by one of the letters s, p, d , or f, each of which correspond to a value of 1 equal to 0,1, 2, or 3 , respectively. The number of electrons having identical values of n and of 1 are indicated by a superscript to the right of the letter. Thus 3p5 indicates that there are 5 electrons d n = 3 and 1 =l. The assigning of quantum numbers to the electrons in the ground state of an atom, and the building up of the periodic system are guided by two well known principles: (a) The Pauli principle, namely, that in one and the same atom no two electrons can have the same four
quantum numbers, the four quantum numbers being n, 1, m, and m,. The symbols m, and m , stand for the magnetic and spin quantum numbers, respectively. (b) In going from one element to the one of next higher atomic number, in the building up of the periodic table, of all the permissible states, the additional electron enters that vacant orbit of $he atom in which it has the lowest energy. Rule (a) limits the maximum number of equivalent electrons, i. e., those having identical values of n and of I. It fixes the maximum number of electrons that can be in any shell or subshell. However, the problem of selecting the particular quantum numbers of the available lowest energy state for the incoming electron still remains. In the building up of the periodic table there are many unoccupied levels available for the entering electron, but rule (b) does not indicate in which one of the unoccupied subshells the incoming electron will have the lowest energy. One must, accep.t the experimental evidence, obtahed chiefly from spectral data, as to which available n and 1 value gives the lowest energy and is taken by the incoming electron. Rules (a) and (b) by themselves do not lead to any method for assigning quantum numbers to the electrons in the building up of the periodic system. A guide to the selection of the proper quantum numbers for an incoming electron in the building up of atoms can be obtained by adding the following to rule f h ) .. The additional electron enters the quantum state with the lowest (n 1) value, and when more than one state having the same (n 1) value i s available the electron selects the state with the lowest n number. I t should be stated a t this point that there are exceptions to this rule, but they are relatively unimportant to the chemist as will be seen later. It is also true t h a t a straightforward quantum mechanical approach to the problem is possible, but accurate solutions of the equations, even for the simplest atoms are extremely difficult. Qualitatively, the quantum mechanical treatment has yielded useful information. For example, from calculations of the eigenfunctions of the 4f and 5f electrons, Mayer (4)concluded that the 4f orbit begins to be filled a t an atomic number of 60 or 61, and that an electron first enters the 5f level in element 91 or 92. Furthermore, even with the spectral data that are \-,
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available the exact distribution of electrons in some elements has not been definitely fixed. The doubtful positions are indicated by the bracketed electrons in the table.* The proposed rule enables one to arrive a t the electron configuration of the ground state of any element. As illustrations, the electron distribution of several elements are worked out. Let us take aluminum with its atomic number, Z =. 13. We start with the configuration for Z = 12: Is2, 2s2, 2p6, 3s2, as can be seen in the table. The next electron could enter the 4s or 3p orbit in addition to a large number of others. The smallest (n 1) value is found to be that of the 3p and 4 s levels. Since both have identical values for (n 1) the electron enters the orbit with the lowest n value which is 3p. Thus, the arrangement of the electrons for aluminum is: l s 2 ,2.9, 2p6, 3s2, 3p1. As another example take the element Indium ( Z = 4 9 ) . Since element 48 has the distribution ls2, 2s2, 2pa, 3s2, 3p6, 3d1°, 4s2, 4pa, 4dr0, 5s2, therefore electron 49 will take on the quantum values 5p. Although the 4f levels are available, the (n + 1 ) value for the 4f level is 7 compared to 6 for the 5p level. As a final illustration element 87 has the configuration
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2 8 18 32 5s' KILIMINI
5p"dlD
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6sPp6p@ 7;
Again it will be seen that levels 5f, 55, 6 4 etc., are available, yet the last added electron has taken up the position 7s in accordance with the proposed energy rule. It can be seen that in each of the above illustrations use is made of the electron distribution of the element with the atomic number Z - 1, z. e., the element preceding the one in question. However, the (n I) rule makes it unnecessary to refer to the preceding element. The Pauli principle limits the maximum number of s, p, d, and f electrons to 6 , 8, 10, and 14, respectively. It will be remembered that the number of terms possible is equal to the numerical value of n, aFnd that the 1 terns are known as s, p, d, and f. To obtain the electron configuration for any atom one may write the symbols for the various levels in the order of their (n 1) values (and when necessary, the n values), as set forth in the proposed (n 1) energy rule, thus: Is, 29, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4 4 etc. Then the superscripts may be entered up to the point where the sum of the superscripts equals the atomic number of the element in question. As an example, for the element antimony (Z = 51) we have Is2, 2sZ,2p6, 3s2, 3pa, 4s2,3d1°, 4pa, 5 9 , 4d1°, 5p3. It is not surprising that there are exceptions to the proposed energy rule or that there are a number of "irregularities" in the table of electron configuration. The relative energies of the various levels available to incoming electrons as well as of those already occupied by electrons must be changed to some extent during the * Spectral data for the transuranium elements appear not to
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building up process. To a first approximation we may say that the entering electron is influenced mainly by the charge on the nucleus, the effect of the neighboring electrons being secondary. However, it appears that in exceptional cases, the energies of the levels predicted by the (n 1 ) rule and the actual levels taken up by incoming electrons have about the sammevalues; and the entrance of the electron into one orbit instead of a very close neighboring one may be considered unimportant from the chemical viewpoint. The energy rule proposed in this article makes it possible to chart the relative energy levels qualitatively as will be seen by viewing the levels in the chart. The rule is successful in indicating the position of the start of every shell or subshell in the electron distribution table except in the case of lanthanum and actinium. It is interesting to note that the energy rule correctly predicts the electron distribution for the rare earths according to the recent values as suggested by Meggers ( 5 ) . Moreover, the existence of a single 5d electron for several members of the rare earths series, as given in most electron distribution tables, is marked "doubtful." The exact agreement between the configuration according to the simple (n 1) energy rule and that suggested by Meggers as indicated in the table should
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JOURNAL OF CHEMICAL EDUCATION Electron Configuration for t h e Ground States of t h e Elements*
55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
Cs Ba La Ce Pr Nd Pmf Sm Eu Gd Tb Dy Ho Er Tm Yb
* Values and symbols compiled from Herzberg,6 Meggers? Babor and Lehmn.1"
f The name Prometheum is not dehitely accepted. The name Cyolonium has also been suggested. (See publication by G. T. Smaom, Am. Scientist, 36, 361 (1948).
DECEMBER, 1948
not be taken too seriously since the energy difference between the 4f and 5d levels is very small (see chart). In connection with this question, Yost, Garner; and Russell (6) state that "the deviations from the expected 4J"5d'6sz configurations are not greatly surprising as the systems are so complex that no definite predictions based on fundamental theory can be made. The general conclusions of chemical interest as to the nature of the rare earth group are not altered." The other exception to the rule in indicating the beginning of a subshell is the case of actinium (2 = 89) which should have a 5f electron. The (n 1) rule predicts the start of a series of elements similar to the rare earth elements beginning withactinium. Although the exact disposition of the valence electrons in actinium is still in doubt, the existence of 8d2 electrons in thorium (Z = 90) strongly suggests a 6d electron in actinium. However, the chemical properties of the transuranium elements are consistent with the conclusion that element 89 (actinium) is the first of a rare earth-like series. This could be due to the filling of the 5f level similar to the filling of the 4f level in the rare earth series. In discussing the transuranium elements, and referring to chemical evidence, Seaborg (7) states that "the evidence strongly indicates that we are dealing here with a transition series of elements in which the 5f electron shell is being filled in a manner similar to the filling of the 4f electron shell in well-known rare earth series. Apparently this new transition series begins with actinium in the same sense that the rare earth series begins with lanthanum. . .." He also states that "the most important criterion for arranging the heavy elements in this series is the probable presence of seven 5f electrons (analogous to the stable gadolmium structure) in tripositive curium (element 96), rather than the
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presence of the first 5f electron in thorium." In another place the same author (8) states that "in the case of some of the elements in the series it may be something of an academic matter to assign electrons to the 5f or 6d shells, as the energy necessary for the shift from one shell to the other may be within the range of chemical binding energies." DISCUSSION
The question might be asked, "How exact are rules (a) and (b) and how do they lead to the periodic recurrence of similar electron configuration?" Regardless of the principles which were used to obtain the distribution of electrons in the ground state of an element, it is true that only experimental data, particularly spectral data, can uniquely and unambiguously yield information regarding the distribution of electrons. Rule (a), the Pauli principle, may be regarded as a generalization deduced from a vast quantity of spectral data. As Herzberg (9) states, "The Pauli principle does not result from the fundamentals of 'quantum mechanics, but is an assumption which, although it fits very well into quantum mechanics, cannot for the time being be theoretically justified." However, there is no evidence of any exception to the Pauli principle. It should be stated that the Pauli principle may be regarded as only one example of a more general principle of nature that was originally formulated by Heisenberg. Historically, the Pauli principle preceded the Heisenberg principle, which states that the complete eigenfunction of a system of two or more electrons must be of an antisymmetric nature. The latter postulate is not only a quantum mechanical formulation of the Pauli principle, as some books would lead us to believe, but it also contains an explanation of many other phy-
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sical and chemical phenomena, e. g., the exchange forces. are specified by the Pauli principle, the next incoming Rule (b) as stated here implies the existence of the electrons cause recurrence of similar configurations. Aufbauprinzip of Bohr and Stoner (II). This rule, Summary. An empirical rule is suggested for ohtaintaken along with the Pauli exclusion principle, actually . ing the electron configuration of an element in its explains the existence of a periodic table. It implies ground state. The proposed rule is simple and reasonthat as electrons are added one by one in "building up" ably correct. an atom, the electrons already existing in the atom are LITERATURE CITED not disturbed from their various states. It means that (1) PAULING,L., "Nature of the Chemical Bonds," Corthe structure of the inner core of successive atoms renell University Press, Itham, New York, 1939. main the same, as is so clearly revealed by the regu(2) PALMER, W. G., "Vdency-Classical and Modern," Cambridge University Press, 1944. D. DE VAULT,J. CHEM. larity of x-ray spectra. Eonc., 21, 526, 575 (1944). This postulate of having the incoming electron in(3) LUDER,W. F., AND S. ZUFFANTI, "Electronic Theory of fluenced only by the nucleus, the other electrons being Acids and Bases," Wiley and Sons, Inc., New York, 1947. merely "screening" electrons, is a very good approxima(4) MAYER,M. G., Phya. Rev., 60, 184 (1941). See also refertion, but only an approximation. Rule (b) can be enoe (5). (5) MEGGERS, W. F., Science, 105, 514 (1947). stated so that it is exact, but then it will not imply the (6) YOST,D. M., C. S. GARNER, AND H. RUSSELL,Jr., "The existence of the Bohr-Stoner "building-up" principle. Rare Earth Elements and Their Compounds," Wiley For example, Moeluyn-Hughes (11) states that "the and Sons, Inc., New York, 1947, p. 3. energy of the atom must he the smallest value consistent (7) SEABORG, G. T., Science, 104, 385 (1946). with the type of nucleus and the number of electrons (8) SEABORG, G. T., Chem. and Eng. News, 23, 2192 (1945). Also see SE~BORG AND WAHL,J. Am. Chem. Soe., 70, concerned." That there is significant interaction be1128 (19481. tween the electrons in building the periodic table is (9) HERZBERG, G., "Atomic Spectra and Atomio Structure," seen in the number of "irregularities," for example, that Dover Publications. New York. 1944. D. 123. of chromium (Z = 24). Rule ( b ) , unlike rule (a) is only GLASSTONE, S., "~hkoreticalchemist&," Van Nostrand Company, he., New York, 1944, p. 93. a good approximation. Moelwyn-Hughes, "Physical Chemistry," Cambridge UniThus, it can be seen that the electron configuration versity Press, 1940, p. 280. of the ground state of the elements should show a cerB a ~ o n ,J. A., AND A. LERRMAN,"Introductory College tain periodicity, because after electrons have filled all Chemistry, 2nd ed. in press, T. Y. Crowell Company, the available positions in a shell, the number of which New Ycrk.
